Which of the following is NOT a characteristic of the standard normal distribution?Select one:a.50% of all values are negative.b.97.5% of all values are greater than -2c.The mean, median and mode are all equal.d.47.5% of all values lie between -1 and 2.
Question
Which of the following is NOT a characteristic of the standard normal distribution?Select one:a.50% of all values are negative.b.97.5% of all values are greater than -2c.The mean, median and mode are all equal.d.47.5% of all values lie between -1 and 2.
Solution
The standard normal distribution has the following characteristics:
a. It is symmetric around zero, so 50% of all values are negative and 50% are positive.
b. 97.5% of all values are greater than -2. This is because the standard deviation is 1, and -2 is two standard deviations below the mean of 0.
c. The mean, median, and mode of a standard normal distribution are all equal to 0.
d. For a standard normal distribution, approximately 68% of the data falls within one standard deviation of the mean (between -1 and 1), 95% falls within two standard deviations (between -2 and 2), and 99.7% falls within three standard deviations (between -3 and 3).
So, the statement that is NOT a characteristic of the standard normal distribution is:
d. 47.5% of all values lie between -1 and 2. This is incorrect because approximately 95% of all values lie between -2 and 2 in a standard normal distribution.
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